The result means George Burley is still seeking his first win as Scotland manager heading into next month's World Cup qualifiers.
Previous encounters against Croatia and the Czech Republic had yielded a draw and a defeat respectively ahead of Wednesday night's clash, with a crucial double-header against Macedonia and Iceland looming.
The Scots' cause was aided when McGivern was dismissed early in the second half, but it was the Irish who could have claimed the win had Healy successfully converted from the penalty spot.
Positives? Burley was able to name star man James McFadden for the first time since taking over as national team manager, while several players made their international debuts.
It was clear right from the outset there would be nothing friendly about this international when 'God Save the Queen' was jeered by the home crowd ahead of kick-off, an act which would have been disheartening for the 7,000 Northern Ireland fans who made the trip.
Once under way, Darren Fletcher was the first to have a go for the Scots, firing wide under pressure from Chris Baird, before debutant Kevin Thomson dragged his shot past the post from long range.
Burley was keen to see McFadden in a Scotland shirt after he had missed the last two games through injury and the Birmingham forward was involved in most of the home side's attacks.
He set up Kenny Miller for the shot in front of goal but Sammy Clingan was first to the ball to clear the danger before the Rangers striker could pull the trigger.
Manchester City's McGivern made his debut for the Irish and quickly became embroiled in a personal battle with Scott Brown, escaping punishment for an earlier challenge before earning the first booking of the game for a second foul on the Celtic midfielder.
McFadden then had a decent chance when he controlled a long ball from Thomson on his chest before squeezing a shot between two white jerseys but the end product was weak and comfortably held by goalkeeper Maik Taylor.
At the other end, the visitors looked dangerous when Chris Brunt slipped a pass through to Healy but his right-footed drive curled just over the crossbar as a disappointing first half ended goalless.
Darren Barr became the first Falkirk player in almost 50 years to represent Scotland when he was thrown into the action after the break, along with goalkeeper Allan McGregor and midfielder Barry Robson.
It was Robson who almost had an immediate impact on the game with a superbly struck effort from distance, which whistled inches over the crossbar.
McGivern had looked assured in the left-back berth but the 18-year-old's debut quickly turned into a night to forget when he was sent off with 56 minutes gone for a second bookable offence after hauling down Brown just outside the box.
There was further drama just three minutes later when McGregor conceded a penalty by felling substitute Warren Feeney in the area only to make amends seconds later by diving to his right to pull off an excellent save to deny Healy's spot-kick.
With just over an hour played, there was another new Scotland cap in the shape of Kris Commons, the Derby winger who qualified through Scottish grandparents and who had been a shock inclusion in Burley's squad.
Burley took full advantage of the opportunity to experiment and Michael Stewart made his first international appearance for more than six years, while his Hearts club-mate Christophe Berra joined the list of debutants.
Only the heroics of Taylor prevented McFadden from snatching a winner.
Robson's corner was nodded on by Barr and the Birmingham forward looked certain to leave the net bulging with a ferocious shot but was denied by an equally impressive block from the goalkeeper.
A long-range shot from Graham Alexander than flashed across the face of goal and was touched just wide of the upright by Taylor as Scotland pressed for a late winner but both nations had to settle for level terms as the game ended goalless.